Risk Is Not Review Value: Wrong-Answer Exposure Under Bounded Review Budgets

Using LLMs as judges has become standard practice for evaluating model outputs at scale. This is particularly common for subjective, open-ended tasks such as assessing helpfulness or alignment, where no single reference answer exists. However, objective tasks introduce a distinct reliability challenge for reference-free LLM judging. In the absence of a reference answer, the judge evaluates factual correctness either through its parametric knowledge or through tool augmentation. Although the former enables efficient evaluation, the judge may hallucinate or lack sufficient evidence for its verdict. Conversely, tool augmentation can provide additional evidence but introduces extra computational cost and requires an appropriate mechanism to determine when and how that evidence should be used reliably. More importantly, neither approach alone provides formal control over the risk of accepted verdicts or guarantees their reliability at a specified level. We propose a risk-controlled framework that calibrates uncertainty thresholds on a held-out set so that the false discovery rate among accepted verdicts remains below a user-specified level~$α$ with high probability, using finite-sample Clopper--Pearson intervals. When the parametric mode is not sufficiently confident, the instance is routed to a retrieval-augmented mode, where the judge gathers web evidence and re-evaluates the instance under a second calibrated threshold. The finite-sample guarantee carries over to this two-threshold routing without additional assumptions. Across open-domain QA benchmarks and judges of varying scales, the framework maintains the target error rate while achieving substantially higher coverage than single-mode baselines.

Qwen3-8B reviewing Llama-3.1-8B in math adds 33.2 points, yet Qwen3-8B alone is 6.4 points more accurate than the result. Reviewing another model's answer is usually judged by its gain over the generator. We show that this confuses verification, which adds accuracy beyond either model alone, with capability transfer, where a stronger reviewer supplies answers it could have given on its own. Measured against the stronger model alone, across 48 pairs of 12 open-weight models (3B to 72B) in math, knowledge, code and reasoning, review beats it in only 9 of 96 review directions, and does worse the larger the capability gap. The reason is anchoring: the reviewer mostly follows the generator, discarding its own correct answers. Review costs 2.6 to 2.8 times as much as the stronger model alone, while a selector using the same two calls is 2.7 to 4.2 points more accurate than review and cheaper. Studies of verification should report the stronger model alone, not only the gain over the generator.

Confidence scores determine whether an LLM answer is accepted, reviewed, or regenerated, yet scalar recalibration can only correct errors visible through the score itself. We introduce RADAR (Repair, Adopt, and Diagnose After Recalibration), a reliability framework that separates confidence repair from deciding whether to deploy the repair and auditing the errors that remain. Under squared loss, we decompose prediction risk into outcome noise, information hidden by the score, and mapping error; restricting repair to order-preserving maps additionally introduces a pooling gap. For repair, we propose Probe-Anchored Isotonic Calibration (PAIC), which learns a monotone map from correctness-probe predictions on unlabeled target prompts. PAIC's excess risk depends on the probe's score-conditional bias and fitting error rather than its overall accuracy. For adoption, we derive a paired procedure with finite-sample control of false improvements. For auditing, we develop a prompt-clustered kernel test that detects feature-aligned residual errors while accounting for dependent answers from the same prompt. Across multiple LLM checkpoints, benchmarks, and distribution shifts, richer predictors can improve confidence estimation, but projecting their information back to a scalar score can lose these gains, and lower prediction risk need not yield better review decisions. Across 47,400 replayed raw-score allocations, paired betting adopts candidates with lower held-out test risk in 42.95% of allocations, versus 15.09% for one-sided empirical Bernstein. RADAR thus provides a principled workflow to repair what a scalar score can express, adopt a repair only when supported by evidence, and diagnose systematic errors that recalibration leaves behind. Code and data will be released upon acceptance.